Definability in Functional Analysis
ثبت نشده
چکیده
The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples. We introduce the notion of deenable real-valued function in functional analysis: a real-valued function f deened on a structure of functional analysis is deenable if it can be \approximated" by formulas which do not involve f. We characterize deenability of real-valued functions in terms of a purely topological condition which does not involve logic.
منابع مشابه
Functional Equations, Constraints, Definability of Function Classes, and Functions of Boolean Variables
The paper deals with classes of functions of several variables defined on an arbitrary set A and taking values in a possibly different set B. Definability of function classes by functional equations is shown to be equivalent to definability by relational constraints, generalizing a fact established by Pippenger in the case A = B = {0, 1}. Conditions for a class of functions to be definable by c...
متن کاملCharacterizing Definability of Second-Order Generalized Quantifiers
We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, the base logic being monadic second-order logic, reduces to the question if a quantifier Q1 is definable in FO(Q2, <,+,×) for certain first-order quantifiers Q1 and Q2. We use our characterization to show new de...
متن کاملTerm Definable Classes of Boolean Functions and Frame Definability in Modal Logic
We establish a connection between term definability of Boolean functions and definability of finite modal frames. We introduce a bijective translation between functional terms and uniform degree-1 formulas and show that a class of Boolean functions is defined by functional terms if and only if the corresponding class of Scott-Montague frames is defined by the translations of these functional te...
متن کاملA Study of Syntactic and Semantic Artifacts and its Application to Lambda Definability, Strong Normalization, and Weak Normalization in the Presence of State
Church’s lambda-calculus underlies the syntax (i.e., the form) and the semantics (i.e., the meaning) of functional programs. This thesis is dedicated to studying man-made constructs (i.e., artifacts) in the lambda calculus. For example, one puts the expressive power of the lambda calculus to the test in the area of lambda definability. In this area, we present a course-of-value representation b...
متن کاملBeth Definability in Institutions
BETH DEFINABILITY IN INSTITUTIONS MARIUS PETRIA∗ AND RĂZVAN DIACONESCU Abstract. This paper studies definability within the theory of institutions, a version of abstract model This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definab...
متن کامل